scholarly journals Local asymptotic normality for normal inverse Gaussian Lévy processes with high-frequency sampling

2012 ◽  
Vol 17 ◽  
pp. 13-32 ◽  
Author(s):  
Reiichiro Kawai ◽  
Hiroki Masuda
Keyword(s):  
Asymptotic Normality ◽  
High Frequency ◽  
Lévy Processes ◽  
Levy Processes ◽  
Local Asymptotic Normality ◽  
Inverse Gaussian ◽  
Frequency Sampling ◽  
High Frequency Sampling ◽  
Normal Inverse Gaussian

Temporal Properties Study of Ocular Wave Aberrations with High Frequency Sampling

2014 ◽  
Vol 34 (7) ◽  
pp. 0733001
Author(s):  
郑贤良 Zheng Xianliang ◽  
刘瑞雪 Liu Ruixue ◽  
夏明亮 Xia Mingliang ◽  
李大禹 Li Dayu ◽  
宣丽 Xuan Li
Keyword(s):  
High Frequency ◽  
Temporal Properties ◽  
Frequency Sampling ◽  
High Frequency Sampling

Multipoint High-Frequency Sampling System to Gain Deeper Insights on the Fate of Nitrate in Artificially Drained Fields

2020 ◽  
Vol 146 (1) ◽  
pp. 06019012 ◽  
Author(s):  
Wenlong Liu ◽  
Bryan Maxwell ◽  
François Birgand ◽  
Mohamed Youssef ◽  
George Chescheir ◽  
...  
Keyword(s):  
High Frequency ◽  
Sampling System ◽  
Frequency Sampling ◽  
High Frequency Sampling

PRICES OF BARRIER AND FIRST-TOUCH DIGITAL OPTIONS IN LÉVY-DRIVEN MODELS, NEAR BARRIER

2011 ◽  
Vol 14 (07) ◽  
pp. 1045-1090 ◽  
Author(s):  
MITYA BOYARCHENKO ◽  
MARCO DE INNOCENTIS ◽  
SERGEI LEVENDORSKIĬ
Keyword(s):  
Financial Markets ◽  
Lévy Processes ◽  
Levy Processes ◽  
Gamma Model ◽  
Asymptotic Results ◽  
Robust Test ◽  
Leading Term ◽  
Digital Options ◽  
Variance Gamma Model ◽  
Normal Inverse Gaussian

We calculate the leading term of asymptotics of the prices of barrier options and first-touch digitals near the barrier for wide classes of Lévy processes with exponential jump densities, including the Variance Gamma model, the KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes. In the case of processes of infinite activity and finite variation, with the drift pointing from the barrier, we prove that the price is discontinuous at the boundary. This observation can serve as the basis for a simple robust test of the type of processes observed in real financial markets. In many cases, we calculate the second term of asymptotics as well. By comparing the exact asymptotic results for prices with those of Carr's randomization approximation, we conclude that the latter is very accurate near the barrier. We illustrate this by including numerical results for several types of Lévy processes commonly used in option pricing.

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